Question

Prove than cos^2(90-x)+cot^2(90-y)+sin^2(90-x)=sec^2y

Answer 1

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Cos²(90-x) + cot²(90-y) + sin²(90-x)




=> here we using this formula

1)Sin²x + cos²x = 1

2) 1 + tan²y = sec²y


${cos}^{2}(90 - x) + {sin}^{2}(90 - x) + {cot}^{2} (90 - y) \\ \\ \: = {sin}^{2}x + {cos}^{2}x + {tan}^{2}y \\ \\ \\ \: = 1 + {tan}^{2}y \: (bcoz \: {sin}^{2} + {cos}^{2}x = 1) \\ \\ \: = {sec}^{2} y \: \: (bcoz \: 1 + {tan}^{2}y = {sec}^{2}y) \\ \\ \\ hope \: it \: helps \: you$